Recently the SWORBHP Medical Council has discussed this very topic. Paramedics should not administer Dimenhydrinate and Diphenhydramine to the same patient.

The main concern here would be a cumulative effect from both medications which could result in an anticholinergic excess clinical toxidrome: dry mouth, mild hyperthermia, tachycardia, dilated pupils, CNS changes (confusion/sedation or paradoxical excitation even seizure).